Collisions of Electrons with Atoms

6 Key excerpts on "Collisions of Electrons with Atoms"

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  eBook - ePub

  Handbook of Deposition Technologies for Films and Coatings

  Science, Applications and Technology

  • Peter M. Martin(Author)
  • 2009(Publication Date)
  • William Andrew

    (Publisher)

  A plasma can be viewed as a medium in which energy is transported both in the gas and also to adjacent surfaces. In the case of a discharge plasma, electrical energy is transmitted, via an electric field, to a gas. The energetic gas particles are then used to promote chemical reactions in the gas or to interact with a surface to produce desirable effects such as surface reordering or sputtering. Thus, the process of energy exchange during collisions involving plasma-produced species is of fundamental importance.

  Gas-phase collision probabilities are often expressed in terms of cross-sections. A related parameter is the mean free path or average distance traveled by particles between collisions. The mean free path λ and collision cross-section σ are generally defined by a simple relationship which treats the particles as hard or impenetrable spheres. The mean free path for energetic particles passing through a gas of particle density N , where the gas particle is at rest is1

  Figure 2.2: Collision cross-sections for electrons in argon. Products Ar+ and Ar+2 (from [2] ), Arm (from [3 , 4 ]), and Ar* (from [4 , 5 ]). Momentum transfer from [6] .

  For electrons, the total collision cross-section can be written as

  where elastic, ex, ion, and attach subscripts indicate elastic, excitation, ionization, and attachment processes. In making plasma calculations it is useful to note the common units and values found in the appendix. In this work, distances are expressed in centimeters (cm), energy in electron volts (eV), and pressure in torr. Figure 2.2 shows the cross-sections for electrons interacting with argon gas. The cross-sections are typically a strong function of the energy of the colliding species. For the case of electrons colliding with room temperature gas particles (atoms or molecules), the kinetic energy of the gas particles is generally much less than that of the electrons and can be neglected (the energy of gas particles at 300 K is approximately 0.039 eV). Consequently, only the electron energy is used in Figure 2.2 . The figure shows that at low electron energies (below the ionization energy of 15.75 eV), the primary collision processes are momentum exchange (σ elastic ) and, to a lesser degree, excitation (σ ex ). At energies considerably larger than the ionization potential, the primary process is ionization (σ ion ). Note that in electronegative gases like oxygen [7] , the halogens, or compounds containing either (e.g. NO, CO, CO2 , CF4 , SiF4 , SF6 ) [8 , 9

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  Physics in Nuclear Medicine E-Book

  • Simon R. Cherry, James A. Sorenson, Michael E. Phelps(Authors)
  • 2012(Publication Date)
  • Saunders

    (Publisher)

  Except for differences in sign, the forces experienced by positive and negative electrons (e.g., β + and β − particles) are identical. There are minor differences between the ionizing interactions of these two types of particles, but they are not of importance to nuclear medicine and are not discussed here. In this chapter, the term electrons is meant to include both the positive and negative types. The annihilation effect, which occurs when a positive electron (positron) has lost all of its kinetic energy and stopped, is discussed in Chapter 3, Section G. The “collisions” that occur between a charged particle and atoms or molecules involve electrical forces of attraction or repulsion rather than actual mechanical contact. For example, a charged particle passing near an atom exerts electrical forces on the orbital electrons of that atom. In a close encounter, the strength of the forces may be sufficient to cause an orbital electron to be separated from the atom, thus causing ionization (Fig. 6-1A). An ionization interaction looks like a collision between the charged particle and an orbital electron. The charged particle loses energy in the collision. Part of this energy is used to overcome the binding energy of the electron to the atom, and the remainder is given to the ejected secondary electron as kinetic energy. Ionization involving an inner-shell electron eventually leads to the emission of characteristic x rays or Auger electrons; however, these effects generally are very small, because most ionization interactions involve outer-shell electrons. The ejected electron may be sufficiently energetic to cause secondary ionizations on its own. Such an electron is called a delta (δ) ray. FIGURE 6-1 Interactions of charged particles with atoms. A, Interaction with an orbital electron resulting in ionization

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  Biomedical Physics in Radiotherapy for Cancer

  • Loredana Marcu, Eva Bezak, Barry Allen(Authors)
  • 2012(Publication Date)
  • CSIRO PUBLISHING

    (Publisher)

  Continuous Slowing Down Approximation ). However, occasional nuclear collision will cause large energy loss and deflection in the trajectory.

  On the other hand, energy losses and changes in directions can be quite large for electrons after the collisions with other electrons and the electron trajectory can be altered significantly during stopping in matter (also known as Energy and Range Straggling ).

  Charged particles lose their energy primarily through two types of interactions: collisional (electronic and nuclear) and radiative:

  1. Collisional interactions.

  (a) Electronic These are inelastic collisions with atomic electrons, resulting in excitation or ionisation. These processes ultimately end with the heating of the absorber (through atomic and molecular vibrations) unless the ions and electrons can be separated using an electric field as is done in radiation detectors.

  (b) Nuclear These are elastic collisions with atomic nuclei; e.g. Rutherford backscattering, nuclear reactions (rare), Moth and Moller scatterings.

  2. Radiative interactions.

  These are type of inelastic collisions where a charged particle undergoes an electromagnetic (Coulomb) interaction with positively charged nuclei. As a result, the particle’s momentum is altered and electromagnetic radiation is emitted (a photon). However, this interaction is important for electrons only. Radiative energy loss is mostly due to bremsstrahlung as the probability of nuclear excitation is quite low.

  1.4.1 Bragg peak

  Charged particles interacting in the absorbing material will leave along their trajectory a trail of ionised matter, electrons and ions (this is actually the basic principle of detecting particles in radiation detectors). Ionised tracks created in a cloud chamber by two protons and some electrons are shown in Figure 1.17

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  eBook - ePub

  Primer on Radiation Oncology Physics

  Video Tutorials with Textbook and Problems

  • Eric Ford(Author)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  r is the distance between the two electrons. This interaction will impart energy to the electrons in the atom, and energy will be lost from the incident electron. This process is called collisional energy loss.

  FIGURE 7.1.1 The two energy loss mechanisms for charged particles.

  The other process is radiative energy loss. As shown in Figure 7.1.1 , an electron incident toward an atom might normally move in straight line as it passes. However, as the electron gets close to the nucleus it experiences the force between two charged particles. Here the force is attractive because the electron has a negative charge and the nucleus has a positive charge. As a result, the trajectory of the electron is bent as it passes the nucleus. This bending is a form of acceleration, and any charged particle undergoing acceleration produces radiation (this will be seen again in future chapters). This process is called radiative energy loss. The photons produced through this process are called “bremsstrahlung” photons (a German word meaning “braking radiation”). Note that we have focused here on an electron interacting with matter but the same forces and interactions apply to heavier charged particles such as the proton or the nucleus of an atom.

  7.1.2 Stopping Power

  There needs to be some system for quantifying the energy lost through the processes described above. Consider the cartoon shown in Figure 7.1.2 . Here an electron is wandering through a medium. As it does so it loses energy through either collisional or radiative processes. The amount of energy loss we write as ΔE , in some length of travel Δx , or in differential form,

  −

  d E

  d x

  . Note that the minus sign is used as a reminder that this is energy loss .

  d E

  d x

  has units of energy loss per unit length or MeV/cm or, as will prove useful later, keV/μm. An intrinsic quantity is more informative in many cases, so we divide the above quantity by the density, ρ , of the medium,

  −

  1 ρ

  d E

  d x

  . This removes the density dependence and makes it easier to directly compare the properties of various materials. This quantity is called the stopping power, S

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  Essentials of Nuclear Medicine Physics and Instrumentation

  • Rachel A. Powsner, Matthew R. Palmer, Edward R. Powsner(Authors)
  • 2013(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  The photoelectric effect is the dominant type of interaction in materials with higher atomic numbers, such as lead (Z = 82). A third type of interaction of photons with matter, pair production, only occurs with very high photon energies (greater than 1020 keV) and is therefore not important in clinical nuclear medicine. Figure 2.1 depicts the predominant types of interaction for various combinations of incident photons and absorber atomic numbers. Figure 2.1 Predominant types of interaction for a range of incident photon energies and absorber atomic numbers. Compton Scattering In Compton scattering, the incident photon transfers part of its energy to an outer-shell or (essentially) “free” electron, ejecting it from the atom. Upon ejection, this electron is called a Compton electron. The photon, which has lost energy in the interaction, is scattered (Figure 2.2) at an angle that depends on the amount of energy transferred from the photon to the electron. The scattering angle can range from nearly 0° to 180°. Figure 2.3 illustrates scattering angles of 135° and 45°. Figure 2.2 Compton scattering. Figure 2.3 Angle of photon scattering. Photoelectric Effect An incident photon may also transfer its energy to an orbital (generally inner-shell) electron. This process is called the photoelectric effect and the ejected electron is called a photoelectron (Figure 2.4). This electron leaves the atom with an energy equal to the energy of the incident gamma ray diminished by the binding energy of the electron

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  Quantum Implications

  Essays in Honour of David Bohm

  • Basil Hiley, F. David Peat, Basil Hiley, F. David Peat(Authors)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  In this article I shall try to put in historical perspective the key physical ideas and mathematical approaches which David Bohm and I used in our development of a collective description of electron interactions in metals during the period 1948–53. This work led to the identification of quantized plasma oscillations as the dominant long-wavelength mode of excitation of electrons in most solids. It justified the application of the independent electron model to the low-frequency motion of electrons in metals, and made possible a consistent and accurate calculation of metallic cohesion. I shall then describe briefly how the extension of those ideas to systems of strongly interacting neutral particles, the helium liquids, has, some thirty years later, enabled us to understand effective particle interactions, elementary excitations and transport in the helium liquids. As a result we now possess a unified picture of excitations and transport in both charged and neutral strongly-interacting quantum many-body systems.

  From Classical to Quantum Plasmas

  Consider a classical plasma; one in which the density and temperature of the electrons are such that their motion may be treated according to the laws of classical mechanics. As we have mentioned, such an electron system displays a high degree of organization, which is manifested in both its screening action and in the coherent high-frequency oscillations known as plasma oscillations. Here we have our first glimpse of the quite different electronic behavior resulting from the many-body character of the problem. We begin with a gas of individual electrons, each of which behaves in isolation as a free particle. We bring the electrons together in a uniform background of positive charge to form the plasma, with, say, an average density of 100 billion electrons per cubic centimeter. We find that as a consequence the electrons no longer behave simply as independent particles; their mutual interaction leads them to screen out any charge disturbance and to carry out the plasma oscillations.

  To understand the screening aspect of the plasma, let us imagine that we have established an imbalance of charge distribution over some region in its interior. We might try to do this by trying to build an artificial cage for the electrons out of the uniform positive charge, since the latter has opposite sign to that of the electrons and so attracts them. If we have an equal density of electrons and positive charge, we have overall charge neutrality in our cage. Now we put more electrons into the cage, building up an excess of negative charge. The electrons then experience a strong mutual repulsion, due to their Coulomb interaction. Their reaction will be a violent one. The excess electrons resent the artificial cage into which they have been put, and lose no time in breaking out. They may accomplish their cage-break with ease, because the energy to finance it comes readily from the strong repulsive interaction. As a consequence, any imbalance in the overall charge distribution is unstable, and the electron system will quickly return to the equilibrium state of charge neutrality.

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